Why Farmers Sometimes Love Risks

Evidence from India

ANNEMIE MAERTENS, DAVID R. JUST,AND A.V. CHARI

WR-902

October 2011

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Why Farmers Sometimes Love Risks: Evidence from

India�

Annemie Maertensy, David R. Just and AV Chari

1 October 2011

�The data were gathered in India during 2007�2008, in collaboration with International Crop ResearchInstitute of the Semi-Arid Tropics (ICRISAT). This research was funded through a NSF Doctoral Disserta-tion Research Improvement Grant (Grant No. 0649330), an AAEA McCorkle Fellowship, a Mario EinaudiCenter for International Studies International Research Travel Grant, a Cornell University Graduate SchoolResearch Travel Grant, an International Student and Scholar O¢ ce Grant and funds provided by AEM andChris Barrett. We thank the numerous research assistants: Sanjit Anilesh, Shraavya Bhagavatula, SanaButool, Madhav Dhere, Anand Dhumale, Meenal Inamdar, Shilpa Indrakanti, Navika Harshe, Sapna Kale,Jessica Lebo, Labhesh Lithikar, Nishita Medha, Ramesh Babu Para, Abhijit Patnaik, Gore Parmeshwar, K.Ramanareddy, P.D. Ranganath and Yu Qin. We thank Marc Bellemare, Chris Barrett, AV Chari, Elaine Liu,Hope Michelson, Ted O�Donoghue, seminar participants at SCC Risk Meeting 2010, and three anonymousreviewers for comments and ideas on a former draft of this paper. Any remaining errors and omissions areour own.

yCorresponding author: Posvar Hall 3204, University of Pittsburgh, Pittsburgh, PA 15260, O¢ ce phone:412-648-7613, E-mail: maertens@pitt.edu

1

Abstract

Using a unique dataset collected among farmers in India�s semi-arid tropics, we document the sur-

prising prevalence of risk-taking behavior in the face of high-stakes gambles. The evidence suggests that

this apparently anomalous behavior is due to a combination of credit constraints and non-convexities in

production. In particular, the high-stakes nature of the gambles creates the potential for a farmer to

undertake a productive investment that would normally be una¤ordable and thereby move to a perman-

ently higher level of income. The degree to which farmers are willing to accept risk in return for this

opportunity appears to relate in an intuitive way to their current agricultural production technology as

well as the demographic composition of their household.

1 Introduction

In developing countries, where the majority of the population depends on agriculture, incomes often display

a considerable amount of variation due to �uctuations in rainfall, disease and pest pressure. As few insurance

possibilities exist,1 attitudes towards risk are crucial determinants of economic decisions and in particular

investment behavior.2

The extensive literature that tries to measure risk attitudes has sometimes inferred them from economic

decisions (see for example, Moscardi and De Janvry 1977 and Antle 1987). Other studies have attempted to

directly elicit preferences over risky distributions (see for example Binswanger 1980, Dillon and Scandizzo

1978, Liu 2008, Just and Lybbert 2009, Yesuf and Blu¤stone 2009). Following in the line of this second strand

of the literature, we conducted experiments to measure the attitudes towards risk among cotton farmers in

three villages in India. These attitudes were elicited via farmers�evaluations of hypothetical (but realistic)

production alternatives involving various risky outcomes. Each alternative was presented as a probability

distribution over cotton yield outcomes. The farmers then indicated their willingness to pay for a bag of

cotton seeds which would result in such a distribution.

The results point to the surprising prevalence of risk-seeking in the households in our sample. As many

as 85% of the sampled farmers expressed a willingness to pay more for riskier distributions. The willingness

to accept risk in return for the potential to achieve high payo¤s bears a strong negative relation to household

wealth. Qualitative as well as statistical evidence suggests that these apparently anomalous results can be

1While several studies have con�rmed the existence of informal insurance networks in village economies (see for instance

Townsend, (1994) for a study in the context of this article), full insurance has not been con�rmed as of yet for households

facing large non-idiosyncratic risk (where risk co-moves within the insurance network). See also Mahul and Wright (2003) for

a discussion on the welfare implications of crop insurance.2The literature on risk in agriculture and risk in the contexts of developing countries is vast, and any attempt to summarize

it would necessarily be incomplete. For an overview, see (among others) Moschini and Hennessy (2001)

1

rationalized by credit constraints in combination with non-convexities in production associated with large

�xed-cost investments. Irrigation and higher education in children appear to be two prominent examples of

such investments.

Our �ndings on risk attitudes are markedly di¤erent from the existing literature, which has by and large

found moderate to large degrees of risk aversion. For example, Binswanger (1980) measures attitudes towards

risk among the same households studied in this article using two methods: an experimental approach with

real and hypothetical payo¤s of various magnitudes and an interview method. The results of the experimental

method indicate that at medium-sized payo¤ levels (equivalent to the monthly salary of an unskilled laborer),

virtually all individuals are moderately risk averse with little variation according to personal characteristics.

He �nds no statistical di¤erence in the risk aversion estimates based on real gambles versus hypothetical

gambles, but a larger coe¢ cient of partial risk aversion when comparing high-stakes gambles to low-stakes

gambles. More recently, Liu (2008), using a low-stakes, real payo¤, experimental method, �nds evidence of

both risk and loss aversion among Chinese cotton farmers, in addition to overweighting of low probabilities.

Yesuf and Blu¤stone (2009) conduct medium-stakes experiments in Ethiopia with real payo¤s set in an

agricultural context. They �nd that depending on the expected payo¤ and range, one-third to two-thirds of

households are severely risk averse.

We believe the distinctiveness of our results is due to the high-stakes involved: for the average farmer in

our sample, achieving the best outcome in the hypothetical distribution would generate over 16,000 rupees

in revenue on a per acre basis, a very sizeable amount that is comparable to the farmer�s annual income.3

At such levels, it appears likely that the tendency to avert risk is over-ridden by the possibility of moving

to a new, permanently higher level of income by undertaking a large investment that would normally be

una¤ordable.

The idea that non-convexities can induce risk-taking, while intuitive, has so far largely remained a

theoretical possibility (see for example Lybbert and Barrett forthcoming and Lybbert et al. 2010). We

believe ours to be the �rst experimental con�rmation of the empirical relevance of this idea. More generally,

this article answers the call of Just and Pope (2003) who argue that many alternative explanations can be

o¤ered for observed behavior under risk, only one of which is curvature of the utility function. The observed

risk response might also be due to technology, physical constraints, or �nancial asymmetries. In order to

properly infer or measure risk aversion from observed choices, one needs to carefully isolate the impacts of

3Dillon and Scandizzo (1978) is the only other paper that we are aware of that has found any evidence of risk-loving behavior

among farmers. They report that a small, but signi�cant fraction of farmers in their study (set in Brazil) could be classi�ed as

risk-loving on the basis of their measure. Although the di¤erence in context, time period and methodology makes comparisons

with our study di¢ cult, it is interesting that their experiment also presented farmers with high-stakes gambles.

2

all these factors.

The paper proceeds as follows: Section 2 describes the study site and the experiment; Section 3 analyzes

the results of the risk experiment; Section 4 presents an illustrative model and Section 5 concludes.

2 Description of the study site and experiment

2.1 Study site

Table 1 introduces the three villages selected for this study. These villages have been followed for over 35

years by the Village Level Studies (VLS) program of the International Crop Research Institute of the Semi-

Arid Tropics (ICRISAT).4 The experimental data were collected by the �rst author in 2007-2008 among 205

of the 246 ICRISAT-VLS respondents in Aurepalle, Kanzara and Kinkhed.5

Aurepalle, with 925 households, is the largest of the three villages. It is located in the drought-prone,

poor, Telangana region of Andhra Pradesh, and in terms of average income is situated between the richer

Kanzara and poorer Kinkhed. Kanzara and Kinkhed, with 319 and 189 households, respectively, are located

in the less drought-prone Akola district of West Maharashtra. The VLS sample includes 128, 63 and 55

households in Aurepalle, Kanzara and Kinkhed, respectively. In both Akola villages, households own, on

average, 5 to 6 acres of land. In Aurepalle, this is signi�cantly less, about 3.2 acres. The average size of a

household is 4 to 5 members in all three villages.

The average education level of the respondent (i.e., the main decision-maker with regard to agriculture) is

low, especially in Aurepalle (2.3 years). It is important to note that in these villages, enrollment in school is

very high (93% of the children between 6 and 15 years are in school), but the rate drops sharply at the higher

education level (21% of the young adults between 19 and 21 years are enrolled in an education institute).

This might be partially due to credit constraints. Higher education can be expensive in India, ranging from

a thousand to a hundred thousand Rs for a degree, yet very few of the farmers in Aurepalle and Kinkhed

report having access to bank credit. In Kanzara 18% have access to bank credit.6

In all three villages, agriculture is one of the main sources of income and cotton is the main cash crop.

Over 80% of the households in Kanzara and Kinkhed farm cotton. In Aurepalle, due to the relatively large

4For an overview of the goals, methods and outcomes of the VLS see: Singh et al. (1985), Walker and Ryan (1990), Bantilan

et al. (2006) and Rao and Charyulu (2007).5We conducted the experiment among the ICRISAT-VLS respondents who have farmed in the recent past or were thinking

of farming in the future. More information on this set of respondents can be found in Appendix A.6While credit is available from other sources, such as input dealers, moneylenders and informal networks (see Besley (1995)

for an introduction), the respondents reported that in terms of large amounts of credit for productive purposes only the banks

(and in some case the company selling the equipment) are an option.

3

number of landless families, this number is lower, 60%.7 The average cotton yield varies strongly from year

to year. In 2007-08, it is around 9 Q/acre in Aurepalle, 3.5 Q/acre in Kanzara and 2 Q/acre in Kinkhed.8

Losses in cotton production in this region are due (among others) to its predominant cultivation under

rainfed conditions: both droughts and, more recently, �oods are an issue. The average cotton yield in

Kanzara and Kinkhed during the last few years was lower in comparison to the period 2001-04, a result

the farmers attribute to excess rainfall and �ooding. In 2007-08, 42%, 30% and 27% of the respondents in

Aurepalle, Kanzara and Kinkhed, respectively, reported having access to irrigation at some point during the

year. Irrigation not only reduces rainfall related risks during the rainy season but also allows for cultivation

during the dry season.9 Both surface water (rivers, canals, ponds and basins) and groundwater (wells)

are used as irrigation sources. The water is applied on the �eld through �ood irrigation, drip irrigation

or sprinkler irrigation. We have no information on the installation of drainage systems, but have data on

whether the farmer perceives waterlogging to be a (general) problem on his plots: fewer than 1% of the

plots are considered to have problems. The cost of a well, irrigation or drainage system is substantial,

amounting to several times the average annual income. In addition, the investment entails risk as not all

wells successfully reach the groundwater table.

2.2 Description of the experiment

The farmers�risk attitudes were assessed by presenting them with a set of hypothetical yield distributions.

While we recognize that the context of the experiment ("framing") is important in terms of interpreting the

results (see Harrison and List 2004) we did not opt for a context-free set-up, the main reason being that it

was exactly this context which made it easy for farmers to imagine this high-stakes decision making process.

The experiments were conducted among all ICRISAT-VLS respondents who had farmed in the past seven

years or who were thinking of farming in the future. Henceforth, we refer to this set of respondents as the

"farmers". Details on the experimental set-up are included in Appendix A.

The risk experiment, based on Lybbert and Just (2007) and Just and Lybbert (2009), consisted of four

hypothetical farming seasons.10 For each "season" the farmer was asked through a verbal exercise based on

7Data of the last seven years.81 Quintal (Q) = 100 kg.9Considering the bene�ts of irrigation in the rainy season, the average pro�t for an irrigated cotton plot is 6,030 Rs/acre

(st. dev. 8,298 Rs/acre) versus 4,051 Rs/acre (st. dev. 5,348 Rs/acre) for an unirrigated plot.10The e¤ect of using hypothetical payments versus real payments has not yet been settled in the literature. The validity

depends on the nature of the experiment and elicitation method. In this case, "the subjects have no special reason to disguise

their true preferences" (Kahneman and Tversky, 1979, p. 265) as their decision has no �nancial consequences. Hence, it

is often considered preferable to use high hypothetical payments over the low real payments that would have been feasible

within the project�s budget. Binswanger (1980), who conducted monetary experiments among the same households as we

4

a Becker-Degroot-Marschak (1964) mechanism his willingness to pay (WTP) for a bag of cotton seed with

a particular yield distribution (su¢ cient to sow one acre of cotton). To deal with illiteracy and innumeracy,

we used a visual method based on Lybbert et al. (2007): Fisher Price building blocks were vertically stacked,

to present the various cotton yield distributions (in quintal (Q) per acre). We use a total of 20 blocks, each

block representing 5%, and three di¤erent colors. Green represents the high yield, i.e., 8 Q/acre. Yellow

represents the average yield, i.e., 6 Q/acre and red represents the low yield, i.e., 4 Q/acre. We started

with two trial distributions to help the farmers learn the game and then did four experiments, in the order

re�ected in table 2.11

We aimed to design the experiment such that the average yields one could obtain were comparable to

what farmers are actually obtaining in the �eld. However, as the average yield on the �eld appeared to vary

a lot from year to year, this was not an easy task. We tried out various speci�cations during the trial round,

�rst basing ourselves on the average yield obtained in the period 2001-2007 (which is about 4 Q/acre, so

the yields o¤ered were 2 Q/acre, 4 Q/acre and 6 Q/acre), but according to the farmers�own account this

was much too low for them to even consider buying these seeds. They explained to us that with the new

genetically modi�ed seeds on the market, the average yields were on the increase. Hence, we decided to

redesign the experiment and base ourselves on their current reference point, i.e., the average yield in 2007-08

was 5.5 Q/acres. Comparing these outcomes with the average yield levels in three villages, one can see that

for the Aurepalle farmers, this distribution is at the lower end of what they are currently achieving, while

for the Akola farmers it is at the higher end, especially for Kinkhed (mainly due to the excess rainfall in the

last few years in Akola). We take into account these potential di¤erences in reference points in the analysis.

The �rst baseline distribution has an expected yield of 6 Q/acre and a variance of 2 Q/acre. The second

distribution has the same expected yield, but a higher variance than the �rst distribution, namely 2.4 Q/acre.

Thus the �rst distribution second-order stochastically dominates the second distribution (SOSD). The third

distribution has a higher expected yield than the �rst one, but also a considerably higher variance, 6.2 Q/acre

did, con�rms that hypothetical and real gambles eliciting risk preferences produce comparable results for low and medium

stakes gambles. However, Holt and Laury (2002), who conducted experiments with students at three US universities, �nd

that respondents behave more risk loving when using hypothetical high stakes (over 100 US dollar) experiments versus real

high-stakes experiment. They conclude that "respondents cannot imagine how they would actually behave under high-incentive

conditions". Both these experiments tried to provide a context-free environment, implying that the di¤erence cannot be due

to framing (Harrison and List, 2004). See also Kuhnberger et al. (2002) and Laury and Holt (2008) for a general discussion.

As the experiment we conducted was framed as a seed buying experience, we suggest that our respondents had less trouble

imagining how they would react.11We did not randomize the order of the distributions. However, as the WTP does not appear to increase systematically as

the experiment progresses (detailed individual results are available on request), we believe that order e¤ects do not play an

important role.

5

and 2.76 Q/acre, respectively. The fourth distribution �rst-order stochastically dominates (FOSD) the �rst

distribution with an expected yield of 6.5 Q/acre and a variance of 1.55 Q/acre, and FOSD a distribution

that SOSD the third distribution. Note also that both the fourth and the third distribution FOSD the

second distribution.

3 Analyzing preferences

3.1 Risk loving behavior

We refer to the lotteries in Table 2 as L1,L2; L3 and L4. We begin with a number of checks of internal

consistency of preferences that follow from First-Order Stochastic Dominance and transitivity (summarized

in Table 3): (1) Anyone who prefers L3 to L4 must also prefer L3 to L1: this turns out to be true 94% of

the time. (2) Further, anyone who prefers L3 to L4, and also prefers L1 to L2 must then also prefer L3 to

L2: this turns out be true 100% of the time. (3) Anyone who prefers L4 to L3 must also prefer L4 to L2:

this happens 100% of the time. (4) Anyone who prefers L1 to L2 must also prefer L4 to L2: this happens

94% of the time, (5) Anyone who prefers L2 to L1 must also prefer L3 to L1: this is true 99% of the time.

So preferences look by and large internally consistent.

We now test the implications of risk-aversion. A risk averse farmer obeying standard expected-utility

theory (EUT) should be willing to pay less for the L2 than for L1, and less for the L3 than for L4. Table

3 shows the percentage of sampled individuals whose stated preferences are in line with these predictions.

Remarkably, only 16% of the respondents appear to be risk averse when choosing between lotteries L1 and

L2. In the intermediate comparison involving L3 and L4, nearly 40% of respondents violate the predictions

of risk aversion. Also remarkable is that nearly 95% of respondents prefer L3 to L1.

To gain a better understanding of what drives WTP, we regress WTP on the probabilities of the distribu-

tions, input costs and output prices12 , education level, and wealth. The intuition behind this is the following:

12To obtain the individual-level output prices and input costs, we regress the output price and input costs of 2007-08 on

numbers of children, numbers of adult household members, acreage of dryland, acreage of irrigated land, soil fertility (how many

plots the farmer has of self-reported good and very good quality), education of the decision maker and a village dummy variable.

The input cost excluded the cost of seed but included the value of family labor and self-produced inputs. Using the predicted

values instead of the actual values has the advantage of providing a value for all farmers, not only the ones who farmed cotton in

2007-08, and of avoiding the bias caused by unobservables correlated with both price and the other explanatory variables in the

main regression (see Appendix C). The average output price is 2,086 Rs/Q (st. dev. 253 Rs/Q). There is little variation among

farmers, but some variation between states (Andhra Pradesh versus Maharashtra). The average cost of inputs, other than seeds

(not including the costs of the quasi-�xed investments such as land and irrigation) is 5,781 Rs/acre (st. dev. 2,942 Rs/acre).

Because the �rst-stage data is available for only a small portion of the sample, clustered bootstrapping causes selection issues

6

If the farmer obeys EU and displays risk aversion, then the magnitude of the e¤ect of increasing the probab-

ility of the best outcome (while reducing the probability of the middle outcome) should be smaller compared

to the e¤ect of increasing the probability of the worst outcome (while reducing the probability of the middle

outcome). Expressed mathematically, de�ne xi as the outcome and pi as the probability of achieving outcome

i. If u0(�) > 0; u00(�) < 0, 0 < x2�x1 = x3�x2 (note that in our case x1 = oQ1�c; x2 = oQ2�c; x3 = oQ3�c

with Q1 = 4; Q2 = 6; Q3 = 8 and o = output price and c = input cost), then:

@WTP

@p1=

u1 � u2u01:p1 + u

02:p2 + u

03:p3

(1)

@WTP

@p3=

u3 � u2u01:p1 + u

02:p2 + u

03:p3

(2)

ju3 � u2j < ju1 � u2j )����@WTP@p3

���� < ����@WTP@p1

���� (3)

with WTP is de�ned as (4):

u(w + outside) =X

pi:u(w �WTP + xi) (4)

where w = initial wealth and outside = outside option (i.e., sowing non-cotton crops).

Table 4 presents the results of this analysis. We approximate the WTP function with a linear model.13

Model 1 includes input costs, output prices, education level, village-level �xed e¤ects and wealth. Model

2 additionally includes the 2007-08 cotton yield as a regressor, as this may in�uence the results by setting

a reference point in the farmer�s mind. Note that the number of observations used to estimate the model

is substantially fewer than model 1 as it includes only the respondents who farmed cotton in 2007-08, as

opposed to all farmers. Model 3 includes farmer-level �xed e¤ects.14

The results in Table 4 indicate that WTP is largely driven by the probability of the best outcome.

Increasing the probability of the best outcome by 10% increases WTP by, on average, 152 to 157 Rs, while

increasing the probability of the worst outcome with the same magnitude decreases WTP by, on average,

32 to 37 Rs. Comparing these with the average and variance of the WTP, respectively, 838 Rs and 493 Rs,

in the second stage. Despite this, the results using the predicted price beliefs from the survey are similar to estimates obtained

by calculating standard errors from full two-stage estimation. In the tables, we opt to report the results using the predicted

price beliefs from the survey directly.13Note also that even when one uses a simple expected utility model to explain the variation in the WTP, the WTP will

depend in a non-linear manner on the characteristics of the distribution of the outside option and the distribution of the gamble

presented to the respondent, the output price and input cost, and the respondent�s preferences with regard to risk.14Recall that each respondent plays the game four times.

7

these numbers are clearly not insigni�cant. As such, it is clear that standard static EUT will not explain

the variation in the data unless farmers are risk loving.

Overall, the three models give very similar results. The yield of the last season (2007-08) has a negative

but statistically insigni�cant e¤ect on WTP in model 2. However, as the regressions include a village-level

�xed e¤ect, one cannot conclude from this result that the reference point has no impact on WTP, as the

village-level �xed e¤ects might be absorbing the majority of this e¤ect.

Increasing the output price of cotton has, as expected, a positive e¤ect on WTP while increasing the input

costs has a negative e¤ect, but neither is signi�cantly di¤erent from zero at the 10% level. We included two

separate wealth controls as asset market imperfections might constrain substitution across types of wealth,

but neither are statistically signi�cant from zero at the 10% level.

The Aurepalle and Kinkhed �xed e¤ects are substantial in magnitude. These �xed e¤ects represent

between village-level variation in climatic conditions, characteristics of the agricultural system (such as

intercropping), the outside options available to the farmer if the "bet"is rejected, or reference point e¤ects.

As the climate and agricultural conditions in Kanzara are similar to the ones in Kinkhed, the positive sign on

the Kinkhed dummy variable could imply that the outside options for farmers in Kinkhed are less favorable

compared to the Kanzara farmers. Education, which could potentially in�uence WTP through changing the

outside option of the farmer, does not appear to have any relation to WTP.

3.2 Correlates of risk-loving behavior

The violations of risk-aversion in the data are striking in terms of what they indicate about the prevalence of

risk-taking behavior. Interviews with the farmers indicated that they were disproportionately attracted to

the possibility of achieving the high payo¤ associated with 8 Q/acre. Some of the farmers explicitly justi�ed

their choices by explaining that if the high outcome were achieved they would be able to invest in large

projects such as irrigation for their farm or higher education for their children.

With this in mind, we now examine some of the correlates of risk-taking behavior. We begin with some

simple summary statistics. We group the respondents into four groups in Table 5: Group I consists of

respondents who are risk-averse in that they prefer L1 to L2 and also prefer L4 to L3; Group II respondents

are moderately risk-seeking in that prefer L2 over L1 but prefer L4 to L3; Group III respondents are extremely

risk-seeking in that they prefer L2 over L1 and also prefer L3 to L4; Group IV is an unusual group in that

these respondents prefer L1 to L2 but then prefer L3 to L4.

Table 5 shows that both wealth and income are negatively correlated with risk-seeking behavior when

we compare groups I, II and III. Interestingly, Group IV respondents appear to be wealthier and have

8

higher incomes than the other groups, which makes us think their stated preferences may not necessarily be

"mistakes" (although we have not found a satisfactory explanation for these preferences). Turning back to

Groups I-III, we �nd that risk-seeking is also associated with more dry land as well as more children who

are currently in school (although neither of these two associations appears statistically signi�cant when we

test the di¤erences in means across groups), which appears to �t with the qualitative evidence. As we would

expect, Group III respondents have a signi�cantly higher valuation for L2 relative to L1 (i.e. WTP2�WTP1)

than Group II respondents.

Consider the di¤erence in WTP between distribution 2 and distribution 1, and the di¤erence in WTP

between distribution 3 and distribution 4, as a measure of willingness to take risks.15 Thus, a positive

di¤erence indicates a risk loving attitude, while a negative di¤erence indicates risk aversion. Figure 1

presents the distribution of these two variables. The mean of the �rst distribution (WTP2 �WTP1) is 85

Rs and the standard deviation is 128 Rs. The mean of the second distribution (WTP3 �WTP4) is -4 Rs

and the standard deviation is 166 Rs.

In �gure 2A we plot the predicted values of (WTP2 �WTP1) and (WTP3 �WTP4) from a regression

of these variables on the total value of assets (see table C2 in the appendix for the regression results), where

we have assumed a quadratic speci�cation. We see that the predicted willingness to assume risk in order to

achieve high outcomes has a U-shaped relationship with wealth. Note however in �gure 2B and the results in

table C2 that the increasing leg of the U shape appears not to be strongly present in the raw data, and only

the decreasing relationship remains. The results are qualitatively similar when using the yield of 2007-08 as

a reference point, or income (results available on request). This shape is inconsistent with prospect theory,

which would predict a positive relationship as wealthier farmers are more prone to loss aversion as their

reference point lies to the right of a less wealthy farmer (Kahneman and Tversky 1979, Starmer 2001).

In Tables 6 and 7 we investigate the relationship between asset composition and the willingness to take on

risks. Table 6 presents the regression results using the di¤erence in WTP between the �rst two distributions

as a measure of willingness to take on risk. The �rst column presents the results of a simple probit regression

in which the dependent variable is 0 or 1 depending on whether the individual prefers L2 to L1. The

second column presents the results of a linear regression model in which the dependent variable is the actual

di¤erence in WTP across the two distributions, and the third column adds quadratic terms to this model.

The fourth column uses the ratio, i.e., (WTP2 �WTP1)=WTP1 as a dependent variable, i.e. we take into

account the variation in WTP1.

The results are qualitatively similar across the various speci�cations. Having an additional child under

the age of 15 years (an additional adult in the household) statistically signi�cantly decreases (increases) the

15Using the language of Just and Lybbert (2009), this is a measure of marginal risk aversion.

9

di¤erence in WTP in most speci�cations. The linear regression estimates these e¤ects at, on average, -15 Rs

for the child and 21 Rs for the adult. Comparing the estimated coe¢ cient on "young adults out of school"

and "young adults in school" it appears that the latter is larger in all speci�cations. The di¤erence in these

coe¢ cients is statistically signi�cantly di¤erent from zero in the quadratic speci�cation and in the probit.

This implies that having a school-going young adult (i.e. over the age of 15 years) in the household increases

the di¤erence in WTP, over the usual increase of having a non school-going young adult of that age in the

household. This average marginal e¤ect is estimated at, on average, 56 Rs in the quadratic speci�cation.

Thus, while adults and children a¤ect the willingness to take on risks through traditional wealth e¤ects,

having a school-going young adult over the age of 15 years increases the willingness to take on risks even

further. Comparing the coe¢ cients on "dryland" and "irrigated land" it appears that the former is larger in

all speci�cations. The di¤erence in these e¤ects is statistically signi�cantly di¤erent from zero in the ratio

speci�cation and in the probit speci�cation, and is estimated in the range of, on average, 2% to 6% in the

linear and the quadratic speci�cation.

Table 7 presents the regression results using the di¤erence in WTP between the third and the fourth

distribution as a measure of willingness to take on risk. Having a school-going young adult in the household

statistically signi�cantly increases the di¤erence in WTP, over the usual increase of having a non-school

going young adult, with, on average, 20 Rs in the linear speci�cation. This di¤erence is only statistically

signi�cantly di¤erent from zero in the quadratic speci�cation. Increasing the dryland owned by one acre

statistically signi�cantly increases the di¤erence in WTP in the probit speci�cation and in the linear spe-

ci�cation (by, on average, about 4 Rs in the latter), but the di¤erence between the coe¢ cient on "dryland"

and "irrigated land" is not statistically signi�cantly di¤erent from zero in any of the speci�cations.

Increasing the output price decreases the di¤erence in WTP. Note that an increase in output price

increases the variance of each distribution. There is little variation in the output price of cotton within

villages, but as the larger farmers tend to fetch a somewhat higher price (as they have better storage, and often

do not need cash urgently), this relatively large e¤ect might partially capture some residual (unobserved)

wealth e¤ects. Increasing the education level of the main decision maker increases the di¤erence in WTP.

Note that, again, the village �xed e¤ects are substantial. In Table 6, the di¤erence between what one pays

for the higher variance gamble and the lower variance gamble is, on average, about 180-185 Rs more for

Kinkhed farmers compared to Kanzara farmers; and, on average, about 268-283 less in Aurepalle. This is

inconsistent with an explanation of loss aversion as for many of the Kinkhed farmers, as opposed to the

Aurepalle farmers, the distributions presented exceed the typical yields they would expect. Finally, it is

worth noting that the wealth variable is generally signi�cant in all regressions, with higher wealth being

associated with lower preference for risk-taking. This suggests that higher education and irrigation may not

10

be the only potential investments that farmers have in mind.

Overall, these results are consistent with the notion that asset dynamics are driving at least some of

the risk behavior within our hypothetical experiment. Individuals could potentially increase their overall

pro�tability through increased education of their children, or by irrigating their land. Irrigated land, on the

other hand, will not be easily improved by added investment.

4 A simple model of risk loving behavior

We outline here a simple illustrative model to capture the idea that non-convexities can induce risk-taking.

Imagine a credit-constrained farmer who lives for two periods and is risk neutral, i.e. his Bernoulli utility

function is a linear function of wealth, and that he can choose each period between a risky technology and

a safe technology.16 In Appendix B we show that the essential logic extends to the case where the farmer is

strictly risk-averse.

If we assume that the two technologies give the same expected pro�t, the farmer will be indi¤erent

between the two in both periods. However, the farmer can also invest in an asset that increases pro�ts in

the second period (this could represent an irrigation project, for example). The farmer may then opt for the

risky technology in the �rst period if the safe technology does not generate enough pro�t to cover the �xed

cost needed for the irrigation project.

It is clear that the potential returns to this investment will depend on the asset position of the farmer.

For instance, a farmer who owns more dryland will - under certain conditions - bene�t more from installing

an irrigation system compared to a farmer who owns less dryland. Similarly, a farmer who has school-going

children of an age where they might bene�t from an investment in higher education, might bene�t more

compared to a farmer who does not have school-going children of that age group.

We purposely abstract from several aspects of the agricultural decision-making process, such as pesticide,

fertilizer and other variable-input decisions. In addition, we assume the farmer is credit-constrained (he has

no access to credit), has a �xed amount of land �L > 0, and during the �rst period has no savings or

irrigation system. For simplicity, we will assume that no storage is possible, so that the only way to transfer

consumption from the �rst period to the second is to invest in the asset. It is important to note that while

we discuss the decision to invest in a new irrigation system, a similar model could apply to any type of large

�xed-cost investment that allows the farmer to move to a superior production function.

Assume that in each time period t 2 f1; 2g, the farmer can choose between two technologies: a �safe�

technology which always yields f(�L;R) where R indicates whether or not the land is irrigated (R 2 f0; 1g),16This model is inspired by the work of Lybbert and Barrett (forthcoming) and Lybbert et al. (2010).

11

and a �risky�technology which yields f(�L;R) + � with probability 1/2 and f(�L;R)� � with probability 1/2,

with � denoting the random component of the production function. Assume that f(�L; 1) > f(�L; 0), i.e.,

irrigation increases average land productivity, and that f(�L;R) � � > 0, i.e., subsistence (de�ned as zero

consumption) is guaranteed even if one obtains the low yield. For simplicity, we assume that the production

function exhibits constant returns to scale, i.e., f(�L; �) = �Lf(1; �) and that no land results in no production,

i.e., f(0; �) = 0. The former assumption implies that we can readily extend the model to the experimental

set-up as we elicited willingness-to-pay for a bag of seeds for one acre of land.17

The per-period Bernoulli utility function is given as u(c), where c denotes consumption. The utility

function is assumed linear, i.e. u(c) = c.18 We assume that a farmer cannot opt for negative consumption.

Acquiring an irrigation system requires a lump sum �xed investment r > 0: We assume that the cost of an

irrigation system is substantial but feasible, and in particular that:

f(�L; 0) + � > r > f(�L; 0) (5)

At the start of the �rst period, the farmer choose between the safe and risky technologies. After the

uncertainty is revealed and the proceeds are obtained, the farmer decides whether or not to invest in the

irrigation technology, and �nally consumes. At the start of the second period, the farmer again makes a

decision between the safe and risky technology, after which the uncertainty is revealed, proceeds are collected

and he consumes.

Let us approach this two-period problem using backward induction, starting from the second period.

From the set-up, it is clear that in the second period the farmer will be indi¤erent between the risky and

safe technologies.

Now note that if the farmer chooses the safe technology in the �rst period, following (5) he will be unable

17Note that if one assumes increasing, or more commonly decreasing, returns to scale, the WTP depends on the amount

of land one has. It is not obvious whether the elicited WTP would in that case refer to the average WTP or the marginal

WTP (of, for instance, the �rst acre of land). Intuitively, an increasing returns to scale production function does not change

the results of the model as the potential returns to the investment can be magni�ed and the results continue to hold for a La;

where � > 0 production functions. However, additional assumptions need to be imposed for the results to continue to hold for

a decreasing returns to scale production function. For a discussion on returns to scale in similar contexts, see Binswanger et

al. (1995) and Ray (1998) for a more general discussion.18For simplicity, we assume that intertemporal utility is additive. A more �exible model could be constructed using Epstein

and Zin�s (1989) non-expected-utility framework for intertemporal choice. This model uses a recursive framework to disassociate

the elasticity of intertemporal substitution and the level of instantanous absolute risk aversion. This stylized model is used

simply to illustrate the potential for moving to a superior production technology after a large investment could lead one to

make risky choices in the current period even if risk-averse. The generality of Epstein-Zin would add no further insight beyond

this, while introducing substantial complication. We thus employ the standard additive utility model.

12

to invest in an irrigation system. However, if the farmer chooses the risky technology in the �rst period and

obtains the high yield, he has the option to invest in an irrigation system. In that case, he will compare the

outcome with irrigation to the outcome without irrigation:

without irrigation:�f(�L; 0) + �

�+ �f(�L; 0) (6)

with irrigation:�f(�L; 0) + �� r

�+ �f(�L; 1)

where � 2 (0; 1) is the discount factor, summarizing preferences over time. The farmer opts for the irrigation

system if and only if:

��f(�L; 1)� f(�L; 0)

�> r (7)

Under conditions (5) and (7),19 the di¤erence in WTP between the risky and safe technology is:

WTPRISKY �WTPSAFE =1

2

�f(�L; 0)� �+ �f(�L; 0)

�+ (8)

1

2

�f(�L; 0) + �� r + �f(�L; 1)

���f(�L; 0) + �(f(�L; 0)

�Rewriting (8):

WTPRISKY �WTPSAFE =1

2

��f(�L; 1)� �f(�L; 0)� r

�(9)

Following (7), (WTPRISKY �WTPSAFE) is strictly positive. Note now that whether (5) and (7) are

satis�ed depends (among other factors) on �L. Assuming that these conditions continue to hold, one could

take the derivative (9) with respect to land, obtaining:

1

2�

�@f(�L; 1)

@L� @f(

�L; 0)

@L

�(10)

Assuming constant returns to scale, expression (10) is strictly positive. Thus, the di¤erence in WTP

increases as one has more dryland. Moreover, this increase in WTP is increasing in the returns to irrigation.

19 (5) and (7) imply that the returns to investment are very large compared to the base return. This condition might be

di¢ cult to meet in a two-period model, but could be easily met if one imagines the increased return to be sustained over a

longer period of time.

13

Conclusion

In this article we have analyzed the relationship between attitudes towards risk and investment possibilities.

We are able to take advantage of a unique data set collected among farmers in India�s semi-arid tropics,

which contains information on farmers�assets and the results of a risk experiment. This risk experiment

consisted of four hypothetical farming seasons. For each season the farmer was asked how much he would

be willing to pay for a bag of cotton seed resulting in a particular yield distribution.

Comparing the willingness to pay for the various yield distributions, we �nd that 85% of the farmers are

willing to pay more for a yield distribution which is second-order stochastically dominated by the baseline

distribution presented to them. Risk-taking behavior appears to be driven by credit constraints in combina-

tion with non-convexities in production. In particular, the potential for investment in higher education and

irrigation are strongly related to risk-taking behavior.

We believe ours is the �rst experimental validation of the notion that non-convexities can generate risk-

taking incentives. We conjecture that the novelty of these results is due to the high-stakes nature of the

gambles, which may be creating a real potential for investment in high-cost projects that overwhelms the

natural tendency to avert risk. One caveat to be borne in mind is that the experiments that we conducted

were context-speci�c and hypothetical. Imitating the experience of a farmer choosing a type of seed in the

input dealer�s shop aided the often illiterate and innumerate respondents to understand the game but did

not allow for an actual payout. It is also not immediately clear that the results of these experiments can be

extrapolated to non-agricultural settings.

14

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18

Appendix A

The experiment was conducted among all households who have made farming decisions in the past seven

years and/or intend to make farming decisions in the future. The reason for this selection is the experiment�s

context-speci�c nature, which would make little sense to non-agricultural households (as we had found out

during the trial round). To obtain responses based on recent experiences, we decided to interview only the

households who farmed within the past seven years, since in that timeframe many new technologies were

introduced, such as genetically modi�ed cotton seeds. The households which did not satisfy these criteria

did not participate in the experiment.

The experiment took place at the end of a 3-5 hour long interview, interrupted with a few tea breaks.

The respondent, who was the main decision-maker with regard to agriculture, received about 1.5 US dollar

for participating in the interview, the equivalent of about one day�s labor. In addition, the respondents in

each village were invited every 2-3 years to participate in a day trip funded by this study together with

other studies. The interview took place in the respondent�s residence. No active e¤ort was undertaken to

separate the respondent from other family members, but as the interview took several hours, only in a few

cases were family members present throughout the interview. For the more subjective questions (such as

this experiment), the respondent was not allowed to discuss the answers with his family members.

The respondent was given ample time to learn the game. As the game was preceded by another game

involving visual representations of a distribution function, the respondents were comfortable with the Fisher-

Price Blocks of various colors. The instructions for the enumerators are given below. The �rst author taught

the enumerators this game, both in a lab setting and subsequently in a �eld setting, so we are con�dent

that all enumerators understood the game and conducted it in the same manner. For each distribution the

farmer was asked to imagine going to the store and buying seeds for this season.

Instructions for the enumerators:

The goal of this part of the questionnaire is to get an idea of the risk aversion of the respondents. This

question is asked of all households who have made farming decisions in the past 7 years and/or intend to

make farming decisions in the future. We will use Fisher Price building blocks to represent yield distributions

of cotton, and ask the respondent how much they would be willing to pay for a bag of these seeds (su¢ cient

for 1 acre of land). Tell the respondent that we will play another game with him/her. You say: �Just like

on your own farm, you will have the chance . buy seeds at the beginning of each season, but not know the

yield until the end of the season. On your own farm, how much you earn depends on whether it is a good

year or a bad year. In this game it is the same. In a good year, you will harvest more, in a bad year you

will harvest less�

19

Then, place the building blocks on the white board. One block represents 5%, requiring a total of 20

blocks for the game.

� The green blocks = high yield (8 quintal/acre) good season

� The yellow blocks = average yield (6 quintal/acre) average season

� The red blocks = low yield (4 quintal/acre) bad season

Explain to the respondent the meaning of the di¤erent blocks. Do several exercises holding up one block,

two blocks etc. to check whether he can associate the percentages with the blocks. Once the respondent

understands the meaning of the blocks, make 2 trial distributions to learn the game. Then proceed with the

4 distributions given in the questionnaire. For each distribution ask how much the respondent is willing to

pay at most, starting from 100 Rs and working your way up in steps of 50 Rs until the farmer changes his

answer. Then, decrease the amount to identify the exact point (to the nearest 5 Rs). After the respondent

has answered, verify and write down the answers (in Rs) in the boxes.

� Trial experiment 1 [100% in low yield]

� Trial experiment 2 [50% in low yield and 50% in average yield]

� Experiment 1 [25% in low yield, 50% in average yield and 25% in high yield]

� Experiment 2 [30% in low yield, 40% in average yield and 30% in high yield]

� Experiment 3 [30% in low yield, 30% in average yield and 40% in high yield]

� Experiment 4 [10% in low yield, 55% in average yield and 35% in high yield]

20

Appendix B

We now lay out the farmer�s decision problem when u00(c) < 0. As before, let us approach this two-period

problem using backward induction, starting from the second period. In the second period, after the farmer has

made his irrigation investment decision, he compares the expected utility of the safe and risky technologies.

As his Bernoulli utility function is (strictly) concave, he opts for the safe technology. Again, if the farmer

chooses the safe technology in the �rst period, following (5), he is unable to invest in an irrigation system.

However, if he chooses the risky technology in the �rst period and obtains the high yield, he has the option

to invest in an irrigation system. In that case, he will compare the outcomes with and without irrigation:

without irrigation: u�f(�L; 0) + �

�+ �u

�f(�L; 0)

�(11)

with irrigation: u�f(�L; 0) + �� r

�+ �u

�f(�L; 1)

�where � 2 (0; 1) is the discount factor, summarizing preferences over time. In this case, the farmer opts for

the irrigation system if and only if:

u�f(�L; 0) + �� r

�+ �u

�f(�L; 1)

�> u

�f(�L; 0) + �

�+ �u

�f(�L; 0)

�(12)

Under conditions (5) and (12), the di¤erence in WTP between the risky and safe technology in the �rst

period is:20

WTPRISKY �WTPSAFE =1

2

�u�f(�L; 0)� �

�+ �u

�f(�L; 0)

��(13)

+1

2

�u�f(�L; 0) + �� r

�+ �u

�f(�L; 1)

����u�f(�L; 0)

�+ �(u

�f(�L; 0)

��The sign of (13) is ambiguous and depends on further assumptions on the returns to the investment.

However, assuming constant returns to scale, and �� > 1, the derivative of (13) with respect to land is

strictly positive. Thus, once more the di¤erence in WTP increases as one has more dryland.

20Note here that we simpli�ed the farmer�s decision making problem by equating the WTP to the discounted expected value,

thereby ignoring the initial wealth. This simplication does not change the main result.

21

Aurepalle Kanzara KinkhedNumber of households in village 925 319 189Number of households in sample 128 63 55Number of households in the experiment 95 57 54Median rainfall (mm/year)¹ 434 748 745Distance to nearest town (km) 10 9 12Average land owned (acre)2 3.4 5.2 6Average dryland owned (acre)2 2.4 2.1 2.6Average irrigated land owned (acre)2 1.0 3.0 3.0Average number of household members 4.23 4.87 4.50Average annual income (Rs)3 43,543 53,720 38,087Average education level of respondent (in years) 2.31 6.61 6.89Average maximum level of education in HH (in years) 7.08 10.41 10% of children enrolled in school4 91 100 95% of young adults enrolled in an educational institute4 32 32 27% of households that farm cotton4 60 84 82Average cotton yield, 2007-08 (Q/acre) 8.97 3.50 1.88Average cotton yield, 2001-045 (Q/acre) 3.53 5.76 4.90Average cotton yield, 2005-075 (Q/acre) 4.46 2.47 3.21Income from agriculture (% of kharif income)6 55 70 66Average seed price non-Bt cotton (Rs/acre)7 650 411 625Average seed price Bt cotton (Rs/acre)7 1,280 929 1,196% of respondents who have access to irrigation 42 30 27% of respondents with access to bank credit8 1.12 17.54 0

Table 1: Basic descriptive statistics of Aurepalle, Kanzara and Kinkhed

Notes: The average/percentage/median statistics refer to the sample in each village in 2007-08 unless otherwise noted; ¹2001-2007; ²Including the landless households who own no land;32004-2005, household-level income as reported in the ICRISAT-VLS; 4Children are defined as being between the ages of 6 and 15 and young adults are defined as being between the ages of 15 and 26; 42001-08; 5Calculated using the ICRISAT-VLS input-output data;

6Based on the income earned from all agriculture related activities at the time of interview during the kharif season (rainy season, the main agricultural season) (this might be an underestimate as not all of the harvest was sold at that point in time); 7This is the average of what respondents - on average - expect a bag sufficient for one acre of seed will cost, note that the expected seed cost varies a lot by cultivar; 8The respondent was asked to imagine he would need credit for agricultural inputs, who would he approach and how likely would he be to receive credit from this individual/organization. Multiple answers were possible. This percentage mentioned here corresponds to the respondents who said they have access to government bank or private bank credit.

Distribution 1 (L₁) Distribution 2 (L₂) Distribution 3 (L₃) Distribution 4 (L₄)4 Q/acre 25 30 30 106 Q/acre 50 40 30 558 Q/acre 25 30 40 35Expected value 6.0 6.0 6.2 6.5Variance 2.0 2.4 2.8 1.6

Table 2: Hypothetical Yield Distributions

Notes: 1 quintal (Q) = 100kg. The table figures represent probabilities multiplied by 100.

Prediction Should be true for.... Validity in the dataL₄≻L₂ For everyone (by FOSD) 96.0%L₄≻L₁ For everyone (by FOSD) 96.0%L₃≻L₂ For everyone (by FOSD) 99.5%L₄≻L₃ For risk averse individuals (by SOSD and then FOSD) 61.0%L₁≻L₂ For risk averse individuals (SOSD) 16.0%L₃≻L₁ Ambiguous 95.0%Note: FOSD = First-Order Stochastic Dominance, SOSD = Second-Order Stochastic Dominance

Table 3: Do farmers obey FOSD and SOSD?

OLS regression / fixed effectsFixed effects

Model 1 Model 2 Model 3Probability to obtain 4 Q/acre -367.34*** -319.63*** -367.34***

(57.40) (39.65) (57.15)Probability to obtain 8 Q/acre 1564.20*** 1527.11*** 1564.20***

(102.29) (107.01) (101.85)Output price, predicted (Rs/Q) -0.18 0.57

(0.80) (0.82)Input costs, predicted (Rs/acre) -0.05 -0.06

(0.06) (0.07)Education level of decision-maker (years) 6.80 2.59

(8.93) (10.00)Wealth (land) per capita (1000 Rs) 0.15 0.12

(0.10) (0.11)Wealth (other assets) per capita (1000 Rs) -0.22 -0.32

(0.46) (0.56)Aurepalle fixed effect 57.38 376.92

(376.13) (438.20)Kinkhed fixed effect 630.83*** 729.28***

(96.55) (121.50)Output produced in 2007-08 (Q/acre) -5.56

(13.49)Constant 856.42 -760.56 416.57***

(1571.07) (1637.15) (33.51)

Table 4: Correlates of Willingness-to-Pay

WTPOLS

Notes: *** p<0.01; ** p<0.05; * p<0.1; standard errors clustered at the individual level are reported in parentheses below the coefficient. Number of observations model 1 = 816; number of observations model 2 = 516; number of observations model 3 = 816. The fixed effects refer to the inclusion of individual level fixed effects. Two observations had missing values, these were not included. The value of other assets was estimated using the 2006-07 ICRISAT data. The results do not change significantly in terms of signs and magnitude of the coefficient if we add a control for rainfall, split up per village or education level. Other assets include livestock, savings, borrowings and lendings, machinery, equipment, other durable goods, and stocks.

Income Wealth Dry Land Irrigated Land Adults Education WTP2-WTP1 WTP3-WTP4 Number(rupees) (rupees) (acres) (acres) 0-15 yrs (yrs)

Out of school In SchoolRisk-averse (I) 66760.60 283.53 2.50 3.73 0.80 0.80 0.20 2.90 8.40 -100.00 -80.00 10(L₁≻L₂ & L₄≻L₃) (15870.77) (100.48) (1.67) (1.17) (0.25) (0.29) (0.13) (0.28) (0.85) (48.30) (35.12)Moderately risk-seeking (II) 53417.52 160.15 2.76 1.39 0.77 0.57 0.32 2.37 2.95 62.57 -91.48 115(L₂≻L₁ & L₄≻L₃) (3814.84) (19.58) (0.26) (0.24) (0.09) (0.09) (0.06) (0.07) (0.35) (6.15) (13.39)Extremely risk-seeking (III) 42985.68 74.95 2.90 2.63 0.88 0.72 0.30 2.65 6.72 214.91 157.89 57(L₂≻L₁ & L₃≻L₄) (5835.84) (16.62) (0.62) (0.67) (0.15) (0.15) (0.07) (0.14) (0.50) (15.22) (13.87)Risk-averse/Risk-seeking (IV) 129781.40 269.37 2.50 5.76 0.50 1.05 0.36 2.55 7.00 -56.82 65.91 22(L₁≻L₂ & L₃≻L₄) (33906.88) (56.86) (1.24) (1.68) (0.17) (0.19) (0.12) (0.24) (1.07) (14.07) (5.83)

Table 5: Characteristics of risk-groupsChildren

15-25 yrs

Notes: Standard errors are in parentheses.

Probit regression Linear regressionWTP2-WTP1 WTP2-WTP1/WTP1

Marginal Effects Model 1 Model 2 Model 3Children -0.101** -15.32** -51.00** -0.016**

(0.049) (8.06) (22.22) (0.008)Children^2 14.18

(9.19)Adults 0.140*** 21.47*** 14.27 0.015**

(0.069) (6.59) (19.90) (0.007)Adults^2 1.40

(2.84)Young adults out of school -0.014 18.87*** 1.05 0.013**

(0.042) (6.62) (14.94) (0.007)Young adults out of school^2 5.19

(4.32)Young adults in school 0.133* 35.23*** 79.4*** 0.030**

(0.092) (12.09) (28.74) (0.012)Young adults in school^2 -24.83**

(12.7)Dryland (acre) 0.030*** 5.04** 6.56** 0.003

(0.015) (2.09) (3.51) (0.002)Dryland (acre)^2 -0.13

(0.15)Irrigated land (acre) 0.001 3.07 0.34 -0.001

(0.008) (1.99) (3.69) (0.002)Irrigated land (acre)^2 0.13

(0.13)Output price, predicted (Rs/Q) -0.005*** -1.05*** -1.03*** -0.001***

(0.002) (0.28) (0.27) (0.000)Input costs, predicted (Rs/acre) 0.000*** 0.03 0.02 0.000**

(0.000) (0.02) (0.02) (0.000)Education of DM (years) 0.042** 7.18** 6.96** 0.005

(0.020) (3.17) (3.22) (0.003)Wealth (other assets) (1000 Rs) -0.001*** -0.05* -0.05* 0.000**

(0.000) (0.03) (0.03) (0.000)Aurepalle fixed effect -283.34* -268.31* -0.262**

(108.34) (108.47) (0.112)Kinkhed fixed effect 0.490*** 185.1*** 180.57*** 0.180***

(0.113) (28.17) (27.48) (0.033)Constant 2083.67*** 2077.87*** 1.973***

(541.24) (530.07) (0.545)

Table 6: Correlates of WTP2-WTP1Linear regression

WTP2-WTP1

Notes: *** p<0.01; ** p<0.05; * p<0.1. DM = decision maker. WTP =willingness-to-pay. Average marginal effects are reported in probit regression where (1=risk loving or risk neutral and 0=risk averse). Robust standard errors are reported in parentheses below the coefficient. Number of observations probit regresstion = 109 (only the Akola villages). Number of observations OLS regression= 204. Children are defined as being between the ages of 6 and 15 and young adults are defined as being between the ages of 15 and 26. The results do not change significantly in terms of size and magnitude of the coefficients if we add a control for rainfall, add the yield of the previous year, split up per village or education level. The (average) marginal effects of "young adults out of school" and "young adults in school" are statistically significantly different from each other at the 1% level in model 2 and at the 5% level in the probit; and the (average) marginal effects of " dryland" and "irrigated land" are statistically significantly different from each other at the 10% level in model 3 and at the 1% level in the probit. See also notes to table 4.

Probit regression Linear regressionWTP3-WTP4 WTP3-WTP4/WTP3

Marginal Effects Model 1 Model 2 Model 3Children 0.067 14.56 -15.21 -0.014**

(0.045) (9.26) (31.06) (0.007)Children^2 11.78

(13.90)Adults 0.018 -4.40 -21.07 0.013**

(0.037) (7.06) (21.52) (0.006)Adults^2 2.62

(3.05)Young adults out of school 0.114*** 10.53 -15.89 0.010**

(0.037) (6.80) (23.89) (0.005)Young adults out of school^2 7.60

(6.57)Young adults in school 0.146** 31.23** 24.71 0.022**

(0.063) (14.01) (34.97) (0.009)Young adults in school^2 4.53

(15.78)Dryland (acre) 0.026** 3.60** 4.24 0.002

(0.012) (1.93) (3.50) (0.002)Dryland (acre)^2 -0.05

(0.19)Irrigated land (acre) 0.024** 3.21 -0.48 0.000

(0.011) (2.87) (3.63) (0.002)Irrigated land (acre)^2 0.17

(0.12)Output price, predicted (Rs/Q) -0.002 -0.47 -0.41 -0.001***

(0.001) (0.33) (0.34) (0.000)Input costs, predicted (Rs/acre) 0.000 0.01 0.01 0.000**

(0.000) (0.04) (0.04) (0.000)Education of DM (years) 0.011 4.13 3.28 0.003

(0.016) (3.29) (3.40) (0.003)Wealth (other assets) (1000 Rs) 0.000* -0.03 -0.03 0.000**

(0.000) (0.03) (0.03) (0.000)Aurepalle fixed effect -0.908** -281.11** -267.30 -0.206**

(0.173) (162.17) (164.48) (0.086)Kinkhed fixed effect 0.067 59.59 53.64 0.140****

(0.121) (49.92) (45.01) (0.021)Constant 970.77 895.32 1.480***

(708.27) (736.90) (0.391)

Table 7: Correlates of WTP3-WTP4Linear regression

WTP3-WTP4

Notes: *** p<0.01; ** p<0.05; * p<0.1. DM = decision maker. WTP =willingness-to-pay. Average marginal effects are reported in probit regression where (1=risk loving or risk neutral and 0=risk averse). Robust standard errors are reported in parentheses below the coefficient. Number of observations = 204. The coefficients on "young adults out of school" and "young adults in school" are statistically significantly different from each other at the 10% level in model 1. See also notes to table 6.

Figure 1A: Histogram of (WTP2-WTP1)

Figure 1B: Histogram of (WTP3-WTP4)Note: one observation of -1500 was dropped to keep a similar scale as in 1A

0.0

02.0

04.0

06.0

08D

ensi

ty

-500 -400 -300 -200 -100 0 100 200 300 400 500WTP2-WTP1

0.0

01.0

02.0

03.0

04.0

05D

ensi

ty

-500 -400 -300 -200 -100 0 100 200 300 400 500 600 700WTP3-WTP4

Figure 2A: Predicted differences in WTP as a function of per capita wealth

Figure 2B: Differences in WTP as a function of per capita wealth

Note: Wealth measure includes livestock, savings, borrowings and lendings, machinery, equipment, other durable goods, stocks and land.

Note: Wealth measure includes livestock, savings, borrowings and lendings, machinery, equipment, other durable goods, stocks and land; one observation of -1500 in WTP3-WTP4was dropped to keep a similar scale as in 1A

-100

-50

050

100

150

Fitte

d va

lues

0 500000 1000000 1500000 2000000Per capita wealth

WTP3-WTP4 WTP2-WTP1

-500

050

010

00

0 500000 1000000 1500000 2000000Per capita wealth

WTP3-WTP4 WTP2-WTP1

Appendix C:

OLS regression output price input cost[Rs/Q] [Rs/acre]

Number of members -11.3 216.8(17.3) (155.8)

Number of adult members 20.3 -230.3(22.3) (199.8)

Dryland (acres) 2.7 -5.7(5.1) (45)

Irrigated land (acres) 3.4 40.6(5.2) (40.9)

Access to a plot of good soil quality 50.8 1044.9(81.2) (712.5)

Number of plots of good soil quality > 1 acre 14 -24.1(20.6) (182.7)

Education level of decision-maker (years) 9.6 -2.7(5.9) (53.7)

Aurepalle fixed effect -211.2*** 3763.8***(57.8) (522.6)

Kinkhed fixed effect -39.8 -799.3(58.2) (508.2)

Constant 2037.1*** 3133.6***(95.1) (836.7)

Table C1: Predicting the individual level output price and input costs

Notes: ** p<0.01; ** p<0.05; * p<0.1; number of observations 130 ; Adj Rsquare output price = 0.23 ; Adj. Rsquare input costs 0.52.

OLS regression WTP2-WTP1 WTP3-WTP4

Per capita wealth (10,000 Rs) -1.83*** -3.53***(0.65) (0.64)

Per capita wealth ^2 0.015*** 0.02*(0.00) (0.00)

Constant 124.05*** 74.52***(12.46) (12.26)

Table C2: Regression results corresponding to Figure 2A

Notes: *** p<0.01; ** p<0.05; * p<0.1; standard errors are reported in parentheses below the coefficient. Number of observations = 204. The dependent variable is the WTP for the second (third) distribution minus the WTP for the first (fourth) distribution in the first (second) column. Wealth includes livestock, savings, land, savings, borrowings, machinery, equipment, other durable goods, and stocks.